Solve the initial value problem. 1 dy y cos 0 Ꮎ ᏧᎾ 4 y + 1 . y(x) = 1

Q: 7. (y + y cos x - ye*) dx + (3x + 3 sin x – 3e*) dy = 0; y (0) = – 1

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Q: 2. Obtain the general solution to the equation dy dx x sin x y cos y

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Q: 6. 3+(e*+3) sin x y tan(x³)-x

A: Solve by differentiation

Q: x = y + 3x¹ sin² (2) to separable equation then solve it. 1. Reduce the DE. x

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Q: Q.5: Solve (1+ y²) dx + x dy – tan-1 y dy = 0.

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Q: - the D.E.: xdy + (2y – x³y² sin(x))dx = 0

A: Given differential equation xdy+2y-x3y2sinxdx=0 which can be written as  dydx=-2y-x3y2sinxx

Q: Solve the IVP. 1. (sin x) y' = (cos x) y + 1, y(7) = 0

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Q: Find dy/dx. 1.y = 5ain a %3D

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Solve (y cos x – 3x²y – 2x)dx + (2y sin x – x° + In y)dy = 0 Solve x sec (ry)dy = -[y sec (xy)…

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Q: Write each equation in the form M(x)dx + N(x)dy = 0 test for exactness and solve those equations…

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Q: 3e da 8. 9. Solve the initial value problem dy cos 5.r, y()=3 de

A: We will use the basic integration formulas to integrate the given integrand.     In second question…

Q: (a) (2e – x)y' = 1.

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Q: 11. Which function has the shortest period? A. y 6 sin(3x) + 20 B. y = 8 cos(2x) - 4 С. y 7 соs(x) +…

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Q: •1/2 | cos(T(x + 1)) dx -2

A: First remove the upper limit and Lower limit and then substitute to make the problem simpler to…

Q: ca/4 4. +1 x cos y dz dx dy

A: Triple integral

Q: Solve 2cos? (x) +3 cos (x)+1=0 for all solutíons osx<2 TT

A: Given 2cos2x+3cosx+1=00≤x≤2π

Q: D Solve the initial value problem. dy dx -=xcos (6x²), y(0)= 7 x² OA. Y=2 y= B. Y= 1 12 1 sin…

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Q: Solve the initial value problem. 4x2. 2 dy (x+ 1)(y + 1)' -X-3 X dx y(1) = 3 ..... The solution is…

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Q: Solve π/2 g(x) = sin x + λ sin x cos t g(t) dt. 0

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Q: Solve the ODE x dx – y – 3x* cos²(), with y(1) = 0. %3D

A: To Determine :-  x dydx -y - 3x4 cos2yx with the initial conditions y1 =0

Q: 1. Solve for y of the Separable D.E. sinx dx +y dy = 0

A: To solve the given differential equation for y.

Q: Find the solution of the equation = e cos y which tends to zero as x→ 00 and has the value cos y…

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Q: .1 Find the value of dz and 8z/ dy at the point A when x changes by (0.01) and y changes by (-0.01)…

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Q: 11. Solve IVP: y" + 2y + 5y = 4e¬ cos(2t), y(0) = 1, y'(0) = 0.

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Q: A rental truck costs $45.45 for a day plus 94¢ per mile. (a) If x is the number of miles driven,…

A: Given that, a rental truck costs $45.45 for a day plus 94c per mile.

Q: S" cos de 4. 2 dx .2 -1 1+x² 5.

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Q: Consider the following initial value problem and without solving the equation determine the largest…

A: the given equation is t2-1y'+sin ty=tt2-9 rewrite y'+sin tt2-1y=tt2-1t2-9 the given equation is of…